Heat oven to 350º.
Spray 8 x 8-inch baking pan with oil.
In a medium bowl, mix 1 cup flour, ¼ cup sugar, and salt until well combined.
Cut butter into flour mixture with a pastry blender until crumbly dough forms.
Press the dough evenly into the bottom of the prepared baking pan. Bake until lightly golden, 10 to 12 minutes.
In a large bowl, whisk egg, egg white, and remaining ½ cup sugar until well combined.
Grate lemon zest and squeeze the juice and add both to the egg mixture.
Add baking powder and the remaining 3 Tbsp. of flour. Mix thoroughly.
Pour the lemon mixture over the cooled shortbread base.
Bake until set and lightly brown at the edges, 20 to 25 minutes.
Cool and dust lightly with confectioners' sugar using a mesh strainer.
Cut into 16 squares.